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There are 12 points in a plane no 3 of which are collinear except that 6 points which are collinear. The number of different triangles formed by joining the straight lines is __________.
  • a)
    220
  • b)
    20
  • c)
    200
  • d)
    None
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
There are 12 points in a plane no 3 of which are collinear except that...
Given information:
- 12 points in a plane
- No 3 points are collinear except for 6 points which are collinear

To find:
- Number of different triangles formed by joining the straight lines

Solution:
- Any 3 non-collinear points will form a triangle. So, we need to find the number of non-collinear points.
- Out of 12 points, 6 points are collinear. So, we can choose any 3 points from the remaining 6 non-collinear points in 6C3 ways.
- Also, we can choose any 2 points from the collinear points and 1 point from the non-collinear points in 6C2 * 6C1 ways.
- So, the total number of triangles formed by joining the straight lines is 6C3 + 6C2 * 6C1 = 200.

Answer: Option C (200)
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There are 12 points in a plane no 3 of which are collinear except that 6 points which are collinear. The number of different triangles formed by joining the straight lines is __________.a)220b)20c)200d)NoneCorrect answer is option 'C'. Can you explain this answer?
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